Exam 3

This is the RMarkdown for Exam 3. Below, we will analyze the BioLogData.

First, Let’s take a look at our data

##     Sample.ID Rep Well Dilution                   Substrate Hr_24 Hr_48 Hr_144
## 1 Clear_Creek   1   A1    0.001                       Water 0.000 0.000  0.000
## 2 Clear_Creek   1   A2    0.001       β-Methyl-D- Glucoside 0.004 0.005  0.004
## 3 Clear_Creek   1   A3    0.001 D-Galactonic Acid γ-Lactone 0.008 0.007  0.001
## 4 Clear_Creek   1   A4    0.001                  L-Arginine 0.003 0.002  0.000
## 5 Clear_Creek   1   B1    0.001   Pyruvic Acid Methyl Ester 0.002 0.000  0.007
## 6 Clear_Creek   1   B2    0.001                    D-Xylose 0.011 0.008  0.021

Here’s a breakdown of the columns in the BioLogData data set:

Column ID	Description
Sample.ID	The location the sample was taken from. There are 2 water samples and 2 soil samples.
Rep	The experimental replicate. 3 replicates for each combination of experimental variables.
Well	The well number on the BioLog plate.
Dilution	The dilution factor of the sample.
Substrate	The name of the carbon source in that well. “Water” is the negative control.
Hr_24	The light absorbance value after 24 hours of incubation.
Hr_48	The light absorbance value after 48 hours of incubation.
Hr_144	The light absorbance value after 144 hours of incubation.

---

• It looks like we need to do some re-arranging of some columns. We’ll do some subsetting and tidying in a bit.

• What are the classes of each column?

## Sample.ID       Rep      Well  Dilution Substrate     Hr_24     Hr_48    Hr_144 
##  "factor" "integer"  "factor" "numeric"  "factor" "numeric" "numeric" "numeric"

• Everything looks good so far. Let’s take a quick look at summaries for each column

##        Sample.ID        Rep         Well        Dilution    
##  Clear_Creek:288   Min.   :1   A1     : 36   Min.   :0.001  
##  Soil_1     :288   1st Qu.:1   A2     : 36   1st Qu.:0.001  
##  Soil_2     :288   Median :2   A3     : 36   Median :0.010  
##  Waste_Water:288   Mean   :2   A4     : 36   Mean   :0.037  
##                    3rd Qu.:3   B1     : 36   3rd Qu.:0.100  
##                    Max.   :3   B2     : 36   Max.   :0.100  
##                                (Other):936                  
##                        Substrate       Hr_24            Hr_48       
##  2-Hydroxy Benzoic Acid     : 36   Min.   :0.0000   Min.   :0.0000  
##  4-Hydroxy Benzoic Acid     : 36   1st Qu.:0.0000   1st Qu.:0.0060  
##  D-Cellobiose               : 36   Median :0.0320   Median :0.2595  
##  D-Galactonic Acid γ-Lactone: 36   Mean   :0.1703   Mean   :0.4691  
##  D-Galacturonic Acid        : 36   3rd Qu.:0.1872   3rd Qu.:0.7220  
##  D-Glucosaminic Acid        : 36   Max.   :2.6500   Max.   :2.7850  
##  (Other)                    :936                                    
##      Hr_144       
##  Min.   :0.00000  
##  1st Qu.:0.04175  
##  Median :0.75200  
##  Mean   :0.92497  
##  3rd Qu.:1.67950  
##  Max.   :3.11600  
## 

Which sample locations are functionally different from each other in terms of what C-substrates they can utilize?

• What are the different sample locations?

## [1] Clear_Creek Soil_1      Soil_2      Waste_Water
## Levels: Clear_Creek Soil_1 Soil_2 Waste_Water

• How many and which substrates are we working with?

##  [1] Water                       β-Methyl-D- Glucoside      
##  [3] D-Galactonic Acid γ-Lactone L-Arginine                 
##  [5] Pyruvic Acid Methyl Ester   D-Xylose                   
##  [7] D-Galacturonic Acid         L-Asparganine              
##  [9] Tween 40                    i-Erythitol                
## [11] 2-Hydroxy Benzoic Acid      L-Phenylalanine            
## [13] Tween 80                    D-Mannitol                 
## [15] 4-Hydroxy Benzoic Acid      L-Serine                   
## [17] α-Cyclodextrin              N-Acetyl-D-Glucosamine     
## [19] γ-Hydroxybutyric Acid       L-Threonine                
## [21] Glycogen                    D-Glucosaminic Acid        
## [23] Itaconic Acid               Glycyl-L-Glutamic Acid     
## [25] D-Cellobiose                Glucose-1-Phosphate        
## [27] α-Ketobutyric Acid          Phenylethylamine           
## [29] α-D-Lactose                 D.L -α-Glycerol Phosphate  
## [31] D-Mallic Acid               Putrescine                 
## 32 Levels: 2-Hydroxy Benzoic Acid 4-Hydroxy Benzoic Acid ... γ-Hydroxybutyric Acid

• Let’s graph the individual sample locations to see what substrates are used in the different conditions

• So it looks like there is quite a bit of variation between the substrates used by the different Sample Locations. It seems also seems to be affected by the amount of light absorption

Are Soil and Water samples significantly different overall (as in, overall diversity of usable carbon sources)? What about for individual carbon substrates?

• In order to see the differences between the substrates’ effects, and the difference between Soil and Water samples, we’ll want to get that previously mentioned tidying done now. It’ll be really easy now that we’ve already subsetted the data.

creek <- creek %>% 
  mutate(status="water")
wastewater <- wastewater %>% 
  mutate(status="water")
soil1 <- soil1 %>%
  mutate(status="soil")
soil2 <- soil2 %>%
  mutate(status="soil")

df <- rbind(creek, wastewater, soil1, soil2)

• Now that we’ve got the columns in the write places, Let’s try creating a model to see if we can view the differences between Soil and Water, and also for the individual substrates.

##                    Df Sum Sq Mean Sq F value   Pr(>F)    
## Substrate          31  143.0    4.61  12.484  < 2e-16 ***
## status              1  237.2  237.20 641.878  < 2e-16 ***
## Substrate:status   31   42.1    1.36   3.674 3.55e-11 ***
## Residuals        3392 1253.5    0.37                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

• Now that we have the model, lets add predictions to our data frame to see how well our model fits the actual data, and how well it predicts the relationship of Substrate and Status on the values.

• The model appears to be predicting pretty well. It doesn’t over-fit the data, and produces p-values for the various substrates that indicate strong statistical significance. Judging by the various p-values, there are significant differences between the Soil and Water based samples, as well as between the individual substrates.

If there are differences between samples, which C-substrates are driving those differences?

• There are differences. The C-Substrates that are driving the differences are can be determined by looking at the model summary above. Those with the higher p-values are driving the difference because they are used the most in that particular environment (water vs. soil)

Does the dilution factor change any of these answers?

• Now that we know that the there is a significant difference between Soil and Water Samples, as well as Substrates individually, lets form some more models to see if Dilution makes any difference. Once we have a few models, we’ll look at a couple simple plots, and model summaries to see if the relationships change because of Dilution.

mod2 <- aov(data=creek, values ~ Substrate * Dilution)
plot(creek$values ~ creek$Dilution)

summary(mod2)

##                     Df Sum Sq Mean Sq F value   Pr(>F)    
## Substrate           31  11.01   0.355   2.744 1.56e-06 ***
## Dilution             1  16.75  16.748 129.373  < 2e-16 ***
## Substrate:Dilution  31  17.06   0.550   4.251 4.22e-13 ***
## Residuals          800 103.57   0.129                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

mod3 <- aov(data=wastewater, values ~ Substrate * Dilution)
plot(wastewater$values ~ wastewater$Dilution)

summary(mod3)

##                     Df Sum Sq Mean Sq F value   Pr(>F)    
## Substrate           31  35.51   1.146   5.215  < 2e-16 ***
## Dilution             1  12.74  12.740  58.000 7.40e-14 ***
## Substrate:Dilution  31  18.78   0.606   2.758 1.37e-06 ***
## Residuals          800 175.72   0.220                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

mod4 <- aov(data=soil1, values ~ Substrate * Dilution)
plot(soil1$values ~ soil1$Dilution)

summary(mod4)

##                     Df Sum Sq Mean Sq F value   Pr(>F)    
## Substrate           31   88.1   2.841   5.320  < 2e-16 ***
## Dilution             1   21.4  21.410  40.090 4.04e-10 ***
## Substrate:Dilution  31   10.1   0.325   0.609    0.955    
## Residuals          800  427.2   0.534                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

mod5 <- aov(data=soil2, values ~ Substrate * Dilution)
plot(soil2$values ~ soil2$Dilution)

summary(mod5)

##                     Df Sum Sq Mean Sq F value Pr(>F)    
## Substrate           31   74.6    2.41    5.53 <2e-16 ***
## Dilution             1   54.0   53.99  124.14 <2e-16 ***
## Substrate:Dilution  31   17.4    0.56    1.29  0.136    
## Residuals          800  347.9    0.43                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

• As we factor in Dilution, we see that the relationships change drastically. As far as the water based sample are concerned, the statistical significance of the difference is unchanged. However, when we look at the differences in the soil based samples, the significance disappears as the p-values rise to over .05.

Do the control samples indicate any contamination?

• Luckily, there is no contamination. The negative control samples for this experiment were all water, and if we look through all of the values for water they are all zero which indicates no contamination.